US8659989B2ActiveUtilityA1
Method and apparatus for waveform independent ranging
Est. expiryFeb 8, 2030(~3.6 yrs left)· nominal 20-yr term from priority
H04L 43/0858
39
PatentIndex Score
0
Cited by
4
References
12
Claims
Abstract
A system and method for calculating a time of arrival (TOA) of an electromagnetic signal is presented. A method receives a fast Fourier transform (FFT) signal that is a FFT of an original electromagnetic signal containing symbol data. The FFT signal is either multiplied or divided with a value to remove the symbol data. Removing the symbol data generates a perturbed data values representing perturbed signal with a perturbed covariance. The method calculates a perturbed covariance of the perturbed data values. After the perturbed covariance is calculated, the method at least partially corrects the perturbed covariance to produce a corrected covariance. The TOA of the original electromagnetic signal is calculated based, at least in part, on the perturbed covariance.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1. A method comprising:
receiving a fast Fourier transform (FFT) signal that is an FFT of an original electromagnetic signal containing symbol data;
multiplying or dividing the FFT signal with a value to remove the symbol data to generate perturbed data values representing a perturbed signal with a perturbed covariance;
calculating a perturbed covariance of the perturbed data values;
after calculating the perturbed covariance, at least partially correcting the perturbed covariance to produce a corrected covariance; and
calculating a time of arrive (TOA) of the original electromagnetic signal based, at least in part, on the corrected covariance.
2. The method of claim 1 further comprising:
calculating a distance based, at least in part, on the corrected covariance; and
locating a transmitting source of the original electromagnetic signal based, at least in part, on the distance.
3. The method of claim 1 wherein the calculating a perturbed covariance further comprises:
applying a smoothing function to the corrected data values to generate an approximation of the perturbed covariance; and
wherein at least partially correcting the perturbed covariance further comprises at least partially correcting the approximation of the perturbed covariance to produce a corrected approximation of the covariance; and
wherein the calculating the TOA of the original electromagnetic signal based, at least in part, on the corrected approximation of the covariance.
4. The method of claim 1 further comprising:
performing an inverse FFT (IFFT) on the perturbed data values to produce time domain data values, wherein the calculating the TOA of the original electromagnetic signal is based, at least in part, on the time domain data values.
5. The method of claim 1 wherein the correcting the perturbed covariance is performed in the time domain.
6. The method of claim 1 further comprising:
reading a reference signal data out of a memory; and
wherein the calculating the perturbed covariance is based, at least in part, on the reference signal data.
7. The method of claim 1 where at least a portion of the method is performed by at least one subspace method of the group of: estimation of signal parameters via rotational invariant techniques (ESPRIT), multiple signal classification (MUSIC) and root-MUSIC.
8. The method of claim 1 wherein the calculating the TOA further comprises:
calculating peak values of the corrected covariance, and wherein the TOA is calculated based, at least in part, on the peak values.
9. The method of claim 1 further comprising:
determining whether the FFT signal needs to be multiplied by complex conjugate values to remove the symbol data and using complex conjugate values to remove the symbol data when the FFT signal needs to be multiplied by complex conjugate values to remove the symbol data.
10. The method of claim 9 wherein the at least partially correcting the covariance further comprise:
at least partially correcting the perturbed covariance with a first method when the FFT signal does not to be multiplied by complex conjugate values to remove the symbol data; and
at least partially correcting the perturbed covariance with a second method that is different than the first method when the FFT signal needs to be multiplied by complex conjugate values to remove the symbol data.
11. The method of claim 1 wherein at least a portion of the method of claim 1 is performed with software.
12. A method for solving for a time of arrival (TOA) of an electromagnetic signal regardless of how the electromagnetic signal is modulated comprising:
defining an output of a receiver a noisy vector
r =D H x + n ,
where D H is a diagonal matrix of tone gains corresponding to a channel frequency response at a tone frequency of [D H ] kk =H(kf 0 ), x is a vector of information symbols and n is an i.i.d. complex Gaussian noise vector, where r may be written in the equivalent form
r =D x h + n
where the k th component of h is H(kf 0 ) and D x is the diagonal information symbol matrix, where information symbols can be stripped by simply multiplying the vector r =D x h + n by D x −1 or D x *;
letting E x denote either D x −1 or D x * where E x represents the values used to strip symbols from r =D x h + n , wherein the received stripped signal is represented by:
{circumflex over (r)} =E x r
where the multi-path channel frequency response is given by complex baseband representation:
H
(
f
)
=
∑
n
=
0
N
α
n
ⅇ
-
j
2
π
(
f
c
+
f
)
τ
n
,
where α n is the n th ray complex gain and τ n is the n th ray delay, wherein the effect of the carrier phase shift, f c τ n , may be absorbed into the arbitrary ray gain's phase without loss of generality, wherein
H
(
f
)
=
∑
n
=
0
N
β
n
ⅇ
-
j
2
π
f
τ
n
,
where the values of [D H ] kk =H(kf 0 ) are
H
(
kf
0
)
=
∑
n
=
0
N
β
n
ⅇ
-
j
2
π
kf
0
τ
n
,
where H(kf 0 ) comprises the samples of a weighted sum of cissoids;
where a signal comprises a sum of tones:
s
(
t
)
=
∑
n
=
0
N
b
n
ⅇ
j
2
π
f
n
t
,
with samples
s
(
kT
0
)
=
∑
n
=
0
N
b
n
ⅇ
j
2
π
kv
n
T
0
,
wherein
θ
n
=
{
f
0
τ
n
T
0
v
n
,
wherein K-dimensional sample vectors are defined as:
v
_
n
=
[
1
ⅇ
j
θ
n
ⅇ
j
2
θ
n
⋮
ⅇ
j
(
K
-
1
)
θ
n
]
,
wherein a corresponding K×N matrix is defined as:
V
=
[
v
_
1
⋮
v
_
2
⋮
⋯
⋮
v
_
N
]
,
where
r =D x V β + n ,
wherein a noisy decision-processed vector is defined by:
r
^
_
=
E
x
D
x
V
β
_
+
E
x
n
_
=
Γ
x
V
β
_
+
μ
_
;
defining a projection of a vector, u, onto the space spanned by a set of vectors as:
û =Ψ c ,
where u , are the columns of the matrix Ψ with c chosen so that
Ψ*( u − û )=0
Ψ* u −Ψ*Ψ c =0,
where
c =(Ψ*Ψ) −1 Ψ* u
û =Ψ(Ψ*Ψ) −1 Ψ* u ;
letting φ be an IDFT matrix and letting φ 1 be its last L row, then
Ψ
=
[
Φ
1
Φ
]
=
[
J
I
]
Φ
,
where
J=[ 0 I 1 ],
and I 1 is the L×L identity matrix where
[
J
I
]
*
[
J
I
]
=
I
+
J
*
J
,
where
Ψ
(
Ψ
*
Ψ
)
-
1
Ψ
*
=
[
J
I
]
Φ
(
Φ
*
(
I
+
J
*
J
)
Φ
)
-
1
Φ
*
[
J
*
I
]
=
[
J
I
]
(
I
+
J
*
J
)
-
1
[
J
*
I
]
,
and where
c =Φ*K u ,
where
K
=
(
I
+
J
*
J
)
-
1
[
J
*
I
]
=
[
2
I
1
0
0
I
]
-
1
[
0
I
0
I
1
0
I
1
]
=
1
2
[
0
2
I
0
I
1
0
I
1
]
,
where is a discrete Fourier transform (DFT) matrix and where
C=Φ*KU;
defining:
x=C d ,
where d represents symbol data of a received electromagnetic signal, wherein when the symbol data is removed without multiplying with a complex conjugate the covariance is represented by:
M {circumflex over (r)} =VM β V*+σ n 2 K,
wherein because K is known, as it depends on C:
M
^
=
K
-
1
2
M
r
^
_
K
-
1
2
=
K
-
1
2
VM
β
_
V
*
K
-
1
2
+
σ
n
2
I
,
wherein the minimizing eigenvectors of M β determine the vectors that are in the null space of V, wherein when ξ is a minimizing vector:
ρ = K −1/2 ξ ;
finding a family { ρ m } of null vectors, wherein the quadratic function is formed as:
ϕ
(
ⅇ
jθ
)
=
∑
m
=
1
M
y
_
*
(
ⅇ
jθ
)
ρ
_
m
2
;
wherein when symbols data can be removed by multiplication with conjugates:
r
^
_
=
E
x
D
x
V
β
_
+
E
x
n
_
=
Γ
x
V
β
_
+
μ
_
,
where:
E x =D x *,
where:
M {circumflex over (r)} = | D x | 2 VM β V*|D x | 2 +σ n 2 | D x | 2 ,
wherein matrix |D x | 2 =P x is diagonal;
defining:
Q
x
=
E
{
[
x
1
2
x
2
2
x
3
2
⋮
x
L
2
]
[
x
1
2
x
2
2
x
3
2
…
x
L
2
]
}
,
where:
M {circumflex over (r)} =Q x ·VM β V*+σ n 2 P x ,
wherein A·B denotes the Schur, or Hadamard, product of matrices A and B, and wherein the matrix P x is given by:
P x =σ d 2 CC*,
wherein matrix Q x is a function of matrix C and can be expressed as:
Q
x
=
D
Q
+
∑
j
=
1
J
q
_
j
q
_
j
*
,
wherein Q x is expressed as a diagonal matrix plus a sum of a small number of rank 1 matrices, wherein when x =C d is unitary, Q x is the sum of a diagonal matrix and a single outer product, with Q x =D Q + qq *;
providing for correlation by providing the additional correction terms q j q j *, wherein is approximated by Q x =D Q + qq *, wherein the x values behave as though the x values are approximately uncorrelated so that correlations that do exist are accounted for;
associating with each vector q j a diagonal matrix D j whose diagonal entries are the components of q j , wherein:
M
r
^
_
=
∑
j
=
1
J
D
j
VM
β
_
VD
j
+
D
Q
·
VM
β
_
V
*
+
σ
n
2
P
x
=
∑
j
=
1
J
D
j
VM
β
_
VD
j
+
D
Q
trace
(
M
β
_
)
+
σ
n
2
P
x
=
∑
j
=
1
J
D
j
VM
β
_
VD
j
+
κ
D
Q
+
σ
n
2
P
x
,
wherein when the rank of V is M, then the rank of
∑
j
=
1
J
D
j
VM
β
_
VD
j
is at most JM;
obtaining L equations with unknowns κ and σ n 2 using the diagonal components of M {circumflex over (r)} =Q x ·VM β V*+σ n 2 P x and solving for κ and σ n 2 , wherein matrix:
F=κD Q +σ n 2 P x
can be computed and factored as:
F=F 1/2 F 1/2 ,
wherein
G
r
_
=
F
-
1
2
M
r
_
F
-
1
2
=
F
-
1
2
∑
j
=
1
J
D
j
VM
β
_
VD
j
F
-
1
2
+
I
,
wherein the first term has a rank at most of JM, wherein the eigenvectors, ξ , of G F , corresponding to the minimum eigenvalue, unity, give the null vectors of the matrix
F
-
1
2
∑
j
=
1
J
D
j
VM
β
_
VD
j
F
-
1
2
,
wherein each eigenvector, ξ , determines a vector:
ρ mj =F −1/2 D j ξ m
lying in the null space of V;
using these vectors ρ mj =F −1/2 D j ξ m , forming a quadratic function:
ϕ
(
ⅇ
jθ
)
=
∑
j
=
1
J
∑
m
=
1
M
y
_
*
(
ⅇ
jθ
)
ρ
_
mj
2
,
the nulls of the quadratic function determine angles corresponding to the delayed signal components; and
determining a TOA based, at least in part, on the angles corresponding to the delayed signal components.Cited by (0)
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